Inertial Quasi-Newton Methods for Monotone Inclusion: Efficient Resolvent Calculus and Primal-Dual Methods

Understand

We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems.

• While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent operator.
• A change of the metric makes its computation hard even for (otherwise in the standard metric) simple operators.
• In order to fully exploit the advantage of adapting the metric, we develop a new efficient resolvent calculus for a low-rank perturbed standard metric, which accounts exactly for quasi-Newton metrics.